IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v208y1994i3p407-422.html
   My bibliography  Save this article

Life-time renormalization in critical dynamics as applied to the isotropic-nematic transition in sidechain liquid crystalline polymers

Author

Listed:
  • Kawasaki, Kyozi
  • Brand, Helmut R.

Abstract

We study the dynamic behavior near the isotropic-nematic transition in liquid crystalline sidechain polymers using a mode coupling technique as applied to the life-time renormalization. To lowest order in mode coupling we find for the dynamical critical exponent z for the relaxation time of the order parameter the value z = 1.5 while in mean field approximation one obtains z = 1. This result is in agreement with recent experiments done in Martinoty's group on two different classes of sidechain liquid crystalline polymers using electric and acoustic birefringence measurements. This qualitative difference in behaviour between low molecular weight systems and sidechain polymers can be traced back to nonlinear (cubic) cross coupling terms in the generalized energy between the order parameter and the strain associated with the transient network. The importance of such nonlinear cross coupling terms is corroborated further by recent measurements of the dynamic stress-optical coefficient in sidechain elastomers.

Suggested Citation

  • Kawasaki, Kyozi & Brand, Helmut R., 1994. "Life-time renormalization in critical dynamics as applied to the isotropic-nematic transition in sidechain liquid crystalline polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(3), pages 407-422.
    • Handle: RePEc:eee:phsmap:v:208:y:1994:i:3:p:407-422
    DOI: 10.1016/0378-4371(94)00059-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719400059X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(94)00059-X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hohenberg, Paul, 1972. "Change in Rural France in the Period of Industrialization, 1830–1914," The Journal of Economic History, Cambridge University Press, vol. 32(1), pages 219-240, March.
    2. Silverberg, Gerald & Lehnert, Doris, 1993. "Long waves and 'evolutionary chaos' in a simple Schumpeterian model of embodied technical change," Structural Change and Economic Dynamics, Elsevier, vol. 4(1), pages 9-37, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Silverberg, Gerald & Verspagen, Bart, 2002. "A Percolation Model of Innovation in Complex Technology," Research Memorandum 032, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    2. Mark Knell & Simone Vannuccini, 2022. "Tools and concepts for understanding disruptive technological change after Schumpeter," Jena Economics Research Papers 2022-005, Friedrich-Schiller-University Jena.
    3. Jan Fagerberg, 2003. "Schumpeter and the revival of evolutionary economics: an appraisal of the literature," Journal of Evolutionary Economics, Springer, vol. 13(2), pages 125-159, April.
    4. Holz, A. & Sorgen, A. & Bennemann, K.H., 1977. "Local critical behaviour at impurities in Ising-type systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(1), pages 145-157.
    5. Safarzynska, Karolina & van den Bergh, Jeroen C.J.M., 2011. "Beyond replicator dynamics: Innovation-selection dynamics and optimal diversity," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 229-245, May.
    6. Giovanni Dosi & Marcelo C. Pereira & Maria Enrica Virgillito, 2017. "The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(2), pages 187-210.
    7. Nayak, Purusottam & Mishra, SK, 2009. "Structural Change in Meghalaya: Theory and Evidence," MPRA Paper 15728, University Library of Munich, Germany.
    8. G. Silverberg, 2007. "Long Waves: Conceptual, Empirical and Modelling Issues," Chapters, in: Horst Hanusch & Andreas Pyka (ed.), Elgar Companion to Neo-Schumpeterian Economics, chapter 50, Edward Elgar Publishing.
    9. Fisher, Michael E. & Au-Yang, Helen, 1980. "Critical wall perturbations and a local free energy functional," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 101(1), pages 255-264.
    10. Cantner, Uwe & Vannuccini, Simone, 2021. "Pervasive technologies and industrial linkages: Modeling acquired purposes," Structural Change and Economic Dynamics, Elsevier, vol. 56(C), pages 386-399.
    11. Giorgio Fagiolo & Paul Windrum & Alessio Moneta, 2006. "Empirical Validation of Agent Based Models: A Critical Survey," LEM Papers Series 2006/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    12. Silverberg, Gerald & Verspagen, Bart, 1999. "Long Memory in Time Series of Economic Growth and Convergence," Research Memorandum 015, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    13. Korzinov, Vladimir & Savin, Ivan, 2018. "General Purpose Technologies as an emergent property," Technological Forecasting and Social Change, Elsevier, vol. 129(C), pages 88-104.
    14. Richard R. Nelson & Sidney G. Winter, 2002. "Evolutionary Theorizing in Economics," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 23-46, Spring.
    15. Safarzyńska, Karolina & Brouwer, Roy & Hofkes, Marjan, 2013. "Evolutionary modelling of the macro-economic impacts of catastrophic flood events," Ecological Economics, Elsevier, vol. 88(C), pages 108-118.
    16. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2022. "Levels of structural change," Journal of Evolutionary Economics, Springer, vol. 32(1), pages 35-86, January.
    17. Uwe Cantner & Simone Vannuccini, 2017. "Innovation and lock-in," Chapters, in: Harald Bathelt & Patrick Cohendet & Sebastian Henn & Laurent Simon (ed.), The Elgar Companion to Innovation and Knowledge Creation, chapter 11, pages 165-181, Edward Elgar Publishing.
    18. Windrum, Paul, 1999. "Simulation models of technological innovation: A Review," Research Memorandum 005, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    19. Dalton, John T. & Leung, Tin Cheuk, 2015. "Dispersion and distortions in the trans-Atlantic slave trade," Journal of International Economics, Elsevier, vol. 96(2), pages 412-425.
    20. P. Windrum, 2007. "Neo-Schumpeterian Simulation Models," Chapters, in: Horst Hanusch & Andreas Pyka (ed.), Elgar Companion to Neo-Schumpeterian Economics, chapter 26, Edward Elgar Publishing.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:208:y:1994:i:3:p:407-422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.